Determine whether the values 10 and 30 are solutions to the quadratic equation (x−27)(x−10)=60 .(1 point)

Question

Responses

Only x=10 is a solution.
Only x equals 10 is a solution.

Neither x=10 nor x=30 is a solution.
Neither x equals 10 nor x equals 30 is a solution.

Only x=30 is a solution.
Only x equals 30 is a solution.

Both x=10 and x=30 are solutions.

Answer 1

To determine whether the values 10 and 30 are solutions to the quadratic equation (x−27)(x−10)=60, we can substitute each value into the equation and see if both sides are equal.

For x = 10:
(10−27)(10−10) = 60
(-17)(0) = 60
0 = 60

Since the equation is not true when x = 10, x=10 is not a solution.

For x = 30:
(30−27)(30−10) = 60
(3)(20) = 60
60 = 60

Since the equation is true when x = 30, x=30 is a solution.

Therefore, the correct response is:
Only x=30 is a solution.